Hierarchical Clustering Sensitivity to Distance Metric Selection Based on Z-Score Normalization

Abstract

This study examines the sensitivity of hierarchical clustering results to the choice of distance metrics using Z-score standardized data from the World Happiness Report. Socio-economic datasets often contain variables with different scales, which can bias distance-based clustering methods if not properly addressed. Therefore, Z-score normalization was applied to ensure each variable contributes equally to the distance computation. The analysis focuses on six socio-economic indicators, namely gross domestic product (GDP), social support, healthy life expectancy, freedom to make life choices, generosity, and perceptions of corruption. Hierarchical clustering was performed using a fixed average linkage method to control the cluster-merging strategy, while three distance metrics Euclidean, Manhattan, and Cosine were compared to evaluate their influence on clustering outcomes. The results demonstrate that the selection of distance metrics affects dendrogram structure, cluster membership, and the relative proximity among countries. Differences across distance metrics were further reflected in internal cluster evaluation using the silhouette coefficient, indicating varying levels of cluster compactness and separation. These findings highlight that, even after proper normalization, distance metric selection plays a critical role in shaping hierarchical clustering results and their interpretation in socio-economic analyses. Overall, the study underscores the importance of methodological consistency and careful metric selection when grouping countries based on multidimensional happiness-related indicators.